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ΧChek is a multi-valued symbolic model-checker [CDE01a,CDEG01]. It is a generalization of an existing symbolic model-checking algorithm to an algorithm for a multivalued extension of CTL (ΧCTL). Given a system and a ΧCTL property, Chek returns the degree to which the system satisfies the property. By multi-valued logic we mean a logic whose values form a finite quasi- boolean distributive lattice. The meet and join operations of the lattice are interpreted as the logical and and or, respectively. The negation is given by a lattice dual-automorphism with period 2, ensuring the preservation of involution of negation (¬¬a = a) and De Morgan laws. For example, a 3-valued logic of abstraction (3), consisting of values true (T), maybe (M), and false (F), is given in Figure 1(a), where the negation operator is defined as: ¬T = F, ¬F = T, and ¬ M = M.

ΧChek: A Multi-valued Model-Checker